Magnetostatic image theory for an arbitrary current loop in front of a permeable sphere

Magnetostatic image theory recently introduced for the problem of a circular current loop in front of a permeable sphere centered on the axis of the loop is generalized to the case of an arbitrary current loop outside the sphere. The theory is derived by finding the image for a current element outside the sphere. As an application, the image for a straight line current is seen to result in a surface current in the form of a circular disk. The present theory is also seen to reproduce that for the circular loop as a special case. The analytic form of the image current is simple enough to be applicable in small-scale computation for problems involving a permeable sphere and stationary current